$\text D = \left[\begin{array}{rr}1 & 0 \\ -1 & 5\end{array}\right]$ and $\text B = \left[\begin{array}{rrr}1 & 0 & 2 \\ 4 & 5 & 4\end{array}\right]$ Let $\text {H = DB}$. Find $\text H$. $ {H = }$
Solution: The Strategy When multiplying matrices, we should find each entry of the resulting product matrix separately. To find entry $(i,j)$ of the resulting product matrix, we calculate the vector dot product of row $i$ of the first matrix and column $j$ of the second matrix. [I don't know what "vector dot product" is!] Finding $\text {H}_{1,1}$ $\text{H}_{1,1}$ is the dot product of the first row of $\text{D}$ and the first column of $\text{B}$. $ \text {H}=\left[\begin{array}{rr}{1} & {0} \\ -1 & 5\end{array}\right]\left[\begin{array}{rr} {1} & 0 & 2 \\ {4} & 5 & 4\end{array}\right]$ Therefore, this is the appropriate calculation of $\text{H}_{1,1}$. $\begin{aligned}\text{H}_{1,1}&=(1,0)\cdot(1,4)\\\\ &=1 \cdot 1 + 0\cdot 4\\\\ &=1 \end{aligned}$ The other entries of $\text{H}$ can be found similarly. Try it yourself for $\text{H}_{2,1}$ What is the appropriate calculation of ${H}_{2,1}$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $-1 \cdot 0 + 5\cdot 5 = 25$ (Choice B) B $1 \cdot 0 + 0\cdot 5 = 0$ (Choice C) C $-1 \cdot 1 + 5\cdot 4= 19$ Check Summary After calculating all the remaining entries of $\text{H}$, we get the following answer. $ \text {H}=\left[\begin{array}{rrr}1 & 0 & 2 \\ 19 & 25 & 18\end{array}\right] $